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Langmuir 2002, 18, 2998-3004
Micellization and Related Behaviors of N-Cetyl-N-ethanolyl-N,N-dimethyl and N-Cetyl-N,N-diethanolyl-N-methyl Ammonium Bromide A. Chatterjee,† S. Maiti,‡ S. K. Sanyal,§ and S. P. Moulik*,† Centre for Surface Science, Department of Chemistry, Jadavpur University, Calcutta-700032, India, College of Pharmacy, 986025 University Medical Center, University of Nebraska Medical Center, Omaha, Nebraska 68198-6025, and Department of Chemical Engineering, Jadavpur University, Calcutta-700032, India Received March 16, 2001. In Final Form: January 17, 2002 The micellization characteristics of N-cetyl-N-ethanolyl-N,N-dimethyl and N-cetyl-N,N-diethanolylN-methyl ammonium bromides have been investigated by microcalorimetric, conductometric, and fluorimetric techniques. The critical micellar concentration (cmc), counterion binding of micelles, their aggregation number, and thermodynamics of micellization have been evaluated at eight different temperatures in the range of 288-323 K. The Gibbs free energy, enthalpy, entropy, and specific heat of the micellization process have been evaluated by the direct calorimetric method as well as by the indirect method of van’t Hoff by processing the cmc results of microcalorimetry and conductometry at different temperatures. The differences of the results obtained by these two procedures have been discussed. The thermodynamic results have been compared with values for the parent compound, N-cetyl-N,N,Ntrimethylammonium bromide, and the effect of the substitution of the ethanolyl group in place of the methyl group on the surfactant head has been rationalized. The effects of the salt NaBr on the thermodynamics of micellization of the studied surfactants have been also studied from the microcalorimetric measurements.
Introduction Surfactants micellize in solution after a critical concentration that depends on their molecular structure and environmental conditions.1-6 For a given tail and under a given environment, the nature of the headgroup essentially controls the micellization process. From the viewpoint of usability, self-organization of a surfactant at a lower concentration is preferable. These make scope for synthesizing new surfactants as well as modifying headgroups of existing surfactants and studying their solution properties with reference to micelle formation. To assess the basics of a surfactant, determinations of its critical micellar concentration (cmc), micellar aggregation number, extent of binding of counterions (for ionic surfactants), shape and mass of the micelle, and polarity of the micellar interior are required. Detailed thermodynamics of the micellization process is also essential for the understanding of its stability and spontaneity of formation and the state of environmental order or disorder. The surfactant, N-cetyl-N,N,N-trimethylammonium bromide (CTAB), is a very commonly used amphiphile; the basics of its micellization and related behaviors have
been essentially studied.5,7-9 It has a moderate cmc value of ∼1 mmol dm-3 at 25 °C and an aggregation number of 55, and the micelle can bind more than 80% counterion.5,7-9 It is quite relevant to study how the introduction of polar groups in place of the methyl groups in its head would influence the micellization and related properties of CTAB. With this end in view, we have herein studied the micellization characteristics of two surfactants, N-cetylN-ethanolyl-N,N-dimethylammonium bromide (CEDAB) and N-cetyl-N,N-diethanolyl-N-methylammonium bromide (CDMAB), employing conductometric and microcalorimetric methods. Their extents of aggregation have been estimated by the fluorimetric method. The results are analyzed in terms of the energetics of the process in comparison to that of CTAB. Experimental Section
* To whom correspondence should be addressed. Fax: 91-334734266. E-mail:
[email protected]. † Centre for Surface Science, Department of Chemistry, Jadavpur University. ‡ College of Pharmacy, University of Nebraska Medical Center. § Department of Chemical Engineering, Jadavpur University.
Materials. The surfactants CEDAB and CDMAB were obtained by the reaction of hexadecyl bromide with a large excess of the corresponding amine in a methanol-acetonitrile (30/70 v/v ratio) mixed solvent under refluxing conditions for 24 h. After removal of the solvent under reduced pressure, the products were recrystallized twice from ethyl acetate. The products were characterized by NMR and mass spectroscopy. The surfactant CTAB was 99% pure product of Fluka, USA, and was used without further purification. The salt NaBr was an A. R. grade product of BDH, India. The pyrene used for the fluorescence measurements was the same purified compound used in earlier studies.8,10,11 The quencher, cetylpyridinium chloride (CPC), was the pure and characterized product of Sigma, USA, used in earlier
(1) Emerson, M. F.; Holtzar, A. J. Phys. Chem. 1967, 71, 3320. (2) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1980. (3) Clint, J. H. Surfactant Aggregation; Chapman and Hall: New York, 1991. (4) Moroi, Y. Micelles: Theoretical and Applied Aspects; Plenum Press: New York, 1992. (5) Moulik, S. P. Curr. Sci. 1996, 71, 368. (6) Kresheck, G. C. Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum Press: New York, 1975: Vol. II, p 95.
(7) Bandyopadhyay, A.; Moulik, S. P.; Dasgupta, P. K. Colloid Polym. Sci. 1989, 267, 1. (8) Moulik, S. P.; Haque, M. E.; Jana, P. K.; Das, A. R. J. Phys. Chem. 1996, 100, 701. (9) Majhi, P. R.; Moulik, S. P. Langmuir 1998, 14, 3986. (10) Majhi, P. R.; Mukherjee, K.; Moulik, S. P.; Sen, S.; Sahu, N. P. Langmuir 1999, 15, 6624. (11) Chatterjee, A.; Dey, T.; Sanyal, S. K.; Moulik, S. P. J. Surf. Sci. Technol., in press.
10.1021/la010404k CCC: $22.00 © 2002 American Chemical Society Published on Web 03/20/2002
Micellization of CEDAB and CDMAB studies.9,11 Doubly distilled water (specific conductance, 2-4 µS cm-1 at 303 K) was used to prepare the solutions. Methods. Conductometry. In the conductance method, a concentrated solution of a surfactant was added in installments with a Hamilton microsyringe in 20 mL of water placed in a wide-mouthed test tube fitted with a dip-type conductivity cell of cell constant 1 cm-1, the assembly being immersed in a constant-temperature water bath (NESLAB, RTE100, USA) with an accuracy of (0.01°. After each addition, the conductance of the solution was measured (after thorough mixing and temperature equilibration) with a Jenway conductometer, U.K. Similar measurements were taken at eight different temperatures at the interval of 5° in the range of 288-323 K and were duplicated. The conductance values were uncertain within the limits of (2%. Microcalorimetry. The microcalorimetric measurements were taken in an OMEGA isothermal titration calorimeter of Microcal Inc. (Northampton, USA). Aliquots of the concentrated surfactant solution (∼15-30 times its cmc) of volume 4-12 µL were injected from a microsyringe (250 µL capacity) at periodic intervals of 4 min in 1.325 mL of water by a computer-controlled delivery arrangement in the cell under a constant stirring condition, and the stepwise heat flow in or out of the cell during the dilution process was recorded.9-23 The addition of the surfactant solution and measurement of the heat were done as programmed in the instrument. The data treatment was performed with the help of Microcal Origin software. The measurements were repeated at least twice to check reproducibility and were performed at eight different temperatures at the interval of 5° in the range of 288323 K by circulating water from a thermostated bath (NESLAB, RTE100, USA) around the adiabatic jacket of the calorimeter cells. The isothermal titration calorimetry (ITC) operative at the microcaloric level is a recent technique and has been amply used by workers in different laboratories15-23 including ours.9-14 The general procedure has been described above with details of the addition procedure in the legends to the concerned figures (Figures 2-4). Fluorimetry. The fluorescence measurements were taken in a Kontron SFM25 fluorometer, Italy, at different temperatures in the range of 293-323 K by circulating water from a thermostated bath (NESLAB, Coolflow25, USA) around the fluorescence cell chamber.10,11 The aggregation numbers were determined from the steady-state quenching24-30 experiments using pyrene (2 µmol dm-3) as the probe and CPC (30-210 µmol dm-3) as the quencher at a total [surfactant] of 50 mmol dm-3 for both CEDAB and CDMAB. The excitation wavelength of pyrene was 334 nm, and the emission extents were recorded in the range of 350-500 nm to determine the micellar aggregation number. The measurements were duplicated to check for reproducibility. (12) Majhi, P. R.; Moulik, S. P. J. Phys. Chem. B 1999, 103, 5977. (13) Majhi, P. R.; Moulik, S. P.; Rodgers, M. P.; Burke, S. E.; Palepu, R. J. Surf. Sci. Technol. 1999, 15, 166. (14) Chatterjee, A.; Moulik, S. P.; Sanyal, S. K.; Mishra, B. K.; Puri, P. M. J. Phys. Chem. B 2001, 105, 12823. (15) Kresheck, G. C.; Vitello, L. B.; Erman, J. E. Biochemistry 1995, 34, 8398. (16) Kresheck, G. C. J. Colloid Interface Sci. 1997, 187, 542. (17) Kresheck, G. C. J. Phys. Chem. 1998, 102, 6596. (18) Blandamer, J.; Cullis, P. M.; Engberts, J. B. F. N. Pure Appl. Chem. 1996, 68, 1577. (19) Onori, G.; Santucci, A. J. Phys. Chem. B 1997, 101, 4662. (20) Blume, A.; Tuchtenhagen, J.; Paula, S. Prog. Colloid Polym. Sci. 1993, 93, 118. (21) Paula, S.; Sus, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742. (22) Majhi, P. R.; Blume, A. Langmuir 2001, 17, 3844. (23) Lah, J.; Pohar, C.; Vesnaver, G. J. Phys. Chem. B 2000, 104, 2522. (24) Turro, N. J.; Yekta, A. J. Am. Chem. Soc. 1978, 100, 5951. (25) Warr, G. G.; Grieser, F. J. Chem. Soc., Faraday Trans. 1 1986, 82, 1813. (26) Moroi, Y.; Humphry-Baker, R.; Gra¨tzel, M. J. Colloid Interface Sci. 1987, 119, 588. (27) Asano, H.; Aki, K.; Ueno, M. Colloid Polym. Sci. 1989, 267, 935. (28) Rodenas, E.; Pe´rez-Benito, E. J. Phys. Chem. 1991, 95, 4552. (29) Tummino, P. J.; Gafni, A. Biophys. J. 1993, 64, 1580. (30) Komaromy-Hiller, G.; Calkins, N.; von Wandruszka, R. Langmuir 1996, 12, 916.
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Figure 1. Conductometric determination of the cmc of CEDAB at different temperatures.
Results and Discussion Critical Micellar Concentration (cmc). The cmc’s of CEDAB and CDMAB were determined by the conductometric and microcalorimetric methods. In the conductance-concentration plots, sharp breaks were obtained indicating the cmc values. Representative plots are illustrated in Figure 1. The ratio of the slopes of the postand pre-cmc straight lines was used to obtain the fraction of the counterions bound (f) to the micelles.14,31-33 The f values with their errors are presented in Tables 1 and 2. The cmc values obtained for CEDAB and CDMAB at eight different temperatures with their errors are presented in Tables 1 and 2, respectively. The microcalorimetric method also produced the cmc from the differential heat of dilution run. A typical illustration of the heat flow, enthalpy of dilution, and the corresponding differential plot against the concentration of the surfactant is presented in Figure 2. The cmc point is indicated in the differential plot. The microcalorimetrically determined cmc values are also included in Tables 1 and 2 for CEDAB and CDMAB, respectively, at eight different temperatures in the interval of 5°. The cmc of CEDAB has been found to be moderately higher than that of CDMAB. The enthalpies of dilution versus the concentrations of CEDAB and CDMAB plots at different temperatures are presented in Figures 3 and 4, respectively. The cmc and the ∆H0m values derived following the procedure described with reference to Figure 2 are also presented in Tables 1 and 2. It is seen from the tables that the cmc’s obtained by the two methods have fair agreement, which is better at higher temperature. The ln Xcmc values of CEDAB and CDMAB versus temperature plots fitted to a second-degree polynomial equation (eq 6) are illustrated in Figure 5. The measurements were taken in the temperature range of 288-323 K at 5° intervals which were reasonably close to derive reliable information on the involved process. The fits of ln Xcmc versus temperature plots for both microcalorimetry and conductometry are reasonably good. The calorimetric curves tend to rise appreciably after showing a tendency of a very shallow minimum toward the lower temperature. But such a tendency of a minimum with respect to temperature is not observed in the conductometric curves. Minima in cmc in the lower range of temperature are (31) Evans, H. C. J. Chem. Soc. 1956, 579. (32) Jana, P. K.; Moulik, S. P. J. Phys. Chem. 1991, 95, 9525. (33) Ghosh, S.; Moulik, S. P. J. Colloid Interface Sci. 1998, 208, 357.
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Table 1. Critical Micellar Concentration and Thermodynamic Parametersa for the Micellization of CEDAB at Different Temperatures ∆H0m/kJ mol-1
cmcc/mM temp/K
fb
cond
calc
288 293 298 303 308 313 318 323
0.737(0.022 0.727(0.022 0.731(0.022 0.704(0.021 0.692(0.021 0.689(0.021 0.679(0.020 0.653(0.020
0.78 ( 0.039 0.78 ( 0.039 0.83 ( 0.041 0.85 ( 0.025 0.91 ( 0.027 0.95 ( 0.028 0.99 ( 0.030 1.07 ( 0.032
0.89(0.044 0.83(0.041 0.86(0.043 0.91(0.027 0.93(0.028 0.97(0.029 1.08(0.032 1.13(0.034
∆G0m/kJ
mol-1
-45.9 -46.8 -47.5 -47.3 -47.7 -48.2 -48.2 -48.0
∆S0m/J K-1 mol-1
∆Cp0m/J K-1 mol-1
van’t Hoffd
cald
van’t Hoff
cal
van’t Hoff
cal
-7.2 -13.5 -19.9 -26.7 -33.8 -41.4 -49.1 -57.1
-6.4 -10.4 -12.0 -15.4 -19.8 -23.1 -24.7 -28.0
134.0 114.0 93.0 68.0 45.0 21.6 -3.01 -28.2
137 124 119 105 91 80 74 62
-1207 -1269 -1331 -1393 -1455 -1517 -1579 -1641
-664 -651 -639 -626 -614 -601 -589 -577
The error limits are ∆G0m ) (3%, ∆H0m(van’t Hoff) ) (5%, ∆H0m(cal) ) (3%, ∆S0m(van’t Hoff) ) (8%, ∆S0m(cal) ) (5%, ∆Cp0m(van’t Hoff) ) (15%, and ∆Cp0m(cal) ) (8%. b The values of the fitting constants a′, b′, and c′ obtained from the second-degree polynomial fitting of the f vs T plot are -0.90363, 0.01283, and -2.47619 × 10-5, respectively. c The values of the fitting constants a, b, and c obtained from the second-degree polynomial fitting of the ln Xcmc (calorimetric cmc) vs T plot are 16.08727, -0.1855, and 3.1672 × 10-4, respectively. d The values of the fitting constants A, B, and C obtained from the second-degree polynomial fitting of the ∆H0 vs T plot are -173.65769, m 2.36396, and -0.0062 (for van’t Hoff) and 287.81896, -1.37953, and 0.001243 (for calorimetry), respectively. a
Table 2. Critical Micellar Concentration and Thermodynamic Parametersa for the Micellization of CDMAB at Different Temperatures ∆H0m/kJ mol-1
cmcc/mM
∆S0m/J K-1 mol-1
∆Cp0m/J K-1 mol-1
temp/K
fb
cond
calc
∆G0m/kJ mol-1
van’t Hoff d
cald
van’t Hoff
cal
van’t Hoff
cal
288 293 298 303 308 313 318 323
0.721(0.022 0.711(0.021 0.704(0.021 0.676(0.020 0.682(0.020 0.668(0.020 0.665(0.020 0.665(0.020
0.72 ( 0.036 0.70 ( 0.035 0.76 ( 0.038 0.78 ( 0.023 0.82 ( 0.025 0.86 ( 0.026 0.94 ( 0.028 1.02 ( 0.031
0.79 ( 0.040 0.77 ( 0.039 0.78 ( 0.039 0.83 ( 0.025 0.84 ( 0.025 0.89 ( 0.027 0.97 ( 0.029 1.04 ( 0.031
-46.0 -46.6 -47.2 -46.9 -47.8 -47.9 -48.2 -48.7
-22.0 -23.1 -24.2 -25.1 -26.2 -27.2 -28.3 -29.5
-5.9 -9.4 -13.3 -16.8 -20.8 -24.4 -26.3 -30.2
83.4 80.3 77.0 72.0 70.0 66.2 62.6 59.3
139 127 114 99 88 75 69 57
-204 -206 -209 -211 -214 -216 -219 -221
-798 -769 -739 -709 -679 -650 -620 -590
a The error limits are ∆G0 ) (3%, ∆H0 (van’t Hoff) ) (5%, ∆H0 (cal) ) (3%, ∆S0 (van’t Hoff) ) (8%, ∆S0 (cal) ) (5%, ∆Cp0 (van’t Hoff) m m m m m m ) (15%, and ∆Cp0m(cal) ) (8%. b The values of the fitting constants a′, b′, and c′ obtained from the second-degree polynomial fitting of the f vs T plot are 5.02984, -0.0267457, and 4.09524 × 10-5, respectively. c The values of the fitting constants a, b, and c obtained from the second-degree polynomial fitting of the ln Xcmc (calorimetric cmc) vs T plot are 13.70443, -0.17079, and 2.93111 × 10-4, respectively. d The values of the fitting constants A, B, and C obtained from the second-degree polynomial fitting of the ∆H0 vs T plot are 16.15543, m -0.06145, and -2.47034 × 10-4 (for van’t Hoff) and 470.78868, -2.51079, and 0.0029731 (for calorimetry), respectively.
presence of the minima in cmc is not observed up to the lower studied temperature of 288 K. The counterion binding extents of both the surfactants are nearly equal; it ranges between 65 and 74% in the temperature range of 35°. The correlation between fCEDAB and fCDMAB is nonlinear. The cmc values of CEDAB and CDMAB by conductance and microcalorimetric methods cond ) - 0.11735 have shown correlative relations of cmcCDMAB cond cal + 1.05291cmcCEDAB and cmcCDMAB ) - 0.00444 + 0.91388 cal cmcCEDAB with correlation coefficients of 0.991 and 0.992, respectively. The slope values of nearly unity signify a nearly equal self-aggregation tendency of the two surfactants. The cmccond and cmccal of both CEDAB and CDMAB have also shown good correlation. Aggregation Number of the Formed Micelles. The micellar aggregation numbers of CEDAB and CDMAB were determined by the static quenching24-30 of the pyrene fluorescence in micellar solutions by the quencher CPC. The following relation was used for the evaluation of the average aggregation number (n j ).11,20,25-30 Figure 2. Titration of 185 µL aliquots of CDMAB solution (14.18 mM) into 1.325 mL of water in 23 steps at the interval of 4 min at 318 K: (A) heat flow vs time; (B) enthalpy change per mole of CDMAB vs [CDMAB]; (C) differential enthalpy change with respect to concentration vs [CDMAB].
normally obtained for ionic surfactants.14,21,34 For the studied surfactants, CEDAB and CDMAB, the distinct (34) Goddard, E. D.; Benson, G. C. Can. J. Chem. 1957, 35, 986.
I0 n j [Q] ln ) I [S] - cmc
(1)
where I and I0 are the fluorescence intensities of pyrene with and without quencher, [S] is the total surfactant concentration in the system, and [Q] is the concentration of the quencher. From the plot of ln I0/I versus [Q] at a constant [S], the n j was determined from the slope. The n j values obtained were 123 and 112 for CEDAB and 105 and 113 for CDMAB
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Figure 3. Microcalorimetric determination of ∆H0m of CEDAB at different temperatures: 288 K, titration of 120 µL aliquots of CEDAB solution (30.91 mM) into 1.325 mL of water in 25 steps; 293 K, titration of 146 µL aliquots of CEDAB solution (30.91 mM) into 1.325 mL of water in 30 steps; 298 K, titration of 97 µL aliquots of CEDAB solution (30.61 mM) into 1.325 mL of water in 21 steps; 303 K, titration of 134 µL aliquots of CEDAB solution (30.61 mM) into 1.325 mL of water in 23 steps; 308 K, titration of 123 µL aliquots of CEDAB solution (30.61 mM) into 1.325 mL of water in 25 steps; 313 K, titration of 105 µL aliquots of CEDAB solution (30.91 mM) into 1.325 mL of water in 23 steps; 318 K, titration of 123 µL aliquots of CEDAB solution (30.91 mM) into 1.325 mL of water in 25 steps; 323 K, titration of 142 µL aliquots of CEDAB solution (30.91 mM) into 1.325 mL of water in 25 steps. All stepwise additions were done at the interval of 4 min.
Figure 4. Microcalorimetric determination of ∆H0m of CDMAB at different temperatures: 288 K, titration of 196 µL aliquots of CDMAB solution (14.18 mM) into 1.325 mL of water in 23 steps; 293 K, titration of 204 µL aliquots of CDMAB solution (14.18 mM) into 1.325 mL of water in 25 steps; 298 K, titration of 120 µL aliquots of CDMAB solution (25 mM) into 1.325 mL of water in 30 steps; 303 K, titration of 100 µL aliquots of CDMAB solution (25 mM) into 1.325 mL of water in 25 steps; 308 K, titration of 120 µL aliquots of CDMAB solution (25 mM) into 1.325 mL of water in 30 steps; 313 K, titration of 112 µL aliquots of CDMAB solution (25 mM) into 1.325 mL of water in 28 steps; 318 K, titration of 185 µL aliquots of CDMAB solution (14.18 mM) into 1.325 mL of water in 23 steps; 323 K, titration of 250 µL aliquots of CDMAB solution (14.18 mM) into 1.325 mL of water in 25 steps. All stepwise additions were done at the interval of 4 min.
at 293 and 323K, respectively. The n j values obtained for both of the surfactants were close and virtually independent of a temperature variation of 30°. Thermodynamics of Micellization. For ionic surfactants, the standard Gibbs energy of micellization, ∆G0m, is obtained from the relation5,14,35,36
∆G0m ) (1 + f)RT ln Xcmc
(2)
where f is the fraction of counterions bound to the micelle and Xcmc represents the cmc in mole fraction units. The relations for the standard enthalpy change, entropy change, and specific heat change of micellization ∆H0m, ∆S0m, and ∆Cp0m respectively are the following:5,14,35,36
d ln Xcmc df - RT2 ln Xcmc (3) dT dT
∆H0m ) -RT2(1 + f) ∆S0m )
∆H0m - ∆G0m T
(4) Figure 5. Temperature-dependent ln Xcmc values of CEDAB and CDMAB by conductometric and calorimetric methods fitted according to a second-degree polynomial equation.
and
∆Cp0m
d∆H0m ) dT
(5)
It is found from Tables 1 and 2 that although the cmc’s obtained by conductometry and calorimetry fairly agree, (35) Mukerjee, P. Adv. Colloid Interface Sci. 1967, 1, 241.
the latter values are to some extent higher than the former. We have used the calorimetric cmc values for the thermodynamic analysis. Our purpose is to compare the (36) Attwood, D.; Florence, A. T. Surfactant Systems, Their Chemistry, Pharmacy and Biology; Chapman and Hall: New York, 1983; pp 72117.
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enthalpy, entropy, and specific heat parameters obtained by the van’t Hoff method of calculation and by the direct processing of the calorimetric results. Very frequently, they do not agree.14,17,37-39 For the evaluation of ∆H0m by the van’t Hoff method, dln Xcmc/dT and df/dT values are required. Both ln Xcmc and f are found to be nonlinear with respect to temperature so that polynomial equations relating ln Xcmc and f with temperature (T) have been used for their evaluation.14,17,19-21 Thus,
ln Xcmc ) a + bT + cT2
(6)
f ) a′ + b′T + c′T2
(7)
and
where a, b, c and a′, b′, c′ are the respective fitting constants for eqs 6 and 7 (the values of the fitting constants a, b, and c as well as a′, b′, and c′ for CEDAB and CDMAB are presented in the footnotes of Tables 1 and 2). From eqs 6 and 7, we have
d ln Xcmc ) b + 2cT dT
(8)
df ) b′ + 2c′T dT
(9)
and
These are used in eq 3 to evaluate ∆H0m according to the final relation
∆H0m ) -RT2[(1 + f)(b + 2cT) + (b′ + 2c′T) ln Xcmc] (10) The fitting eq 11 has been used to relate ∆H0m with T.
∆H0m ) A + BT + CT2
(11)
where A, B, and C are the fitting constants (the values of the fitting constants A, B, and C are also presented in the footnotes of Tables 1 and 2). The differential form of eq 11 has been used to obtain ∆Cp0m. Thus,
∆Cp0m
d∆H0m ) ) B + 2CT dT
(12)
All polynomial fittings have been processed in a computer using the Microcal Origin software. We have also examined another form of fitting equation used by Kresheck,17 which was also tried by us on a previous occasion.14 As before, the results derived by these two methods have nice agreement. The set of eqs 6-12 described above has, therefore, been used in deriving the thermodynamic information. The results with limits of their errors are presented in Tables 1 and 2. In Figure 6, comparisons of ∆H0m values obtained from (1) microcalorimetry, (2) the microcalorimetric cmc processed according to the van’t Hoff method using eq 3 that (37) Kresheck, G. C.; Hargraves, W. A. J. Colloid Interface Sci. 1974, 48, 481. (38) Franks, F.; Reid, D. S. Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum Press: New York, 1975: Vol. II, p 337. (39) Naghibi, H.; Tamura, A.; Sturtevant, J. M. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 5597.
Figure 6. Comparison of temperature-dependent enthalpy of micellization of CEDAB and CDMAB evaluated in different ways. CEDAB: (a) direct microcalorimetry; (b) microcalorimetric cmc’s processed at different temperatures by the van’t Hoff method with f; (c) conductometric cmc’s processed at different temperatures by the van’t Hoff method with f. CDMAB: (d) direct microcalorimetry; (e) microcalorimetric cmc’s processed at different temperatures by the van’t Hoff method with f; (f) conductometric cmc’s processed at different temperatures by the van’t Hoff method with f.
is, eq 10, and (3) the conductometric cmc treated by the van’t Hoff method in a similar way are illustrated. The results obtained by procedures 1 and 2 have significant disagreement between them; those between procedures 2 and 3 have modest disagreement. The disagreement widens with increasing temperature in the case of CEDAB, and it narrows down toward higher temperature for CDMAB. In the former, the microcalorimetric results merge at 288 K, whereas all the three results merge at 323 K for the latter. The ∆S0m values derived from eq 4 by combining the ∆G0m obtained from eq 2 with the abovedescribed ∆H0m values are illustrated in Figure 7. The same trends as for ∆H0m have been observed for both CEDAB and CDMAB. Like other reported self-organizing systems (micelles and microemulsions), the ∆H0m and ∆S0m nicely compensate between them.40-43 The results of the present study have revealed excellent correlations (plots are not shown) with compensation temperatures of 286 and 294 K for CEDAB and CDMAB micellization, respectively. Such a phenomenon is possible owing to the small variation of ∆G0m in the studied temperature range of 35°: the major part of the associated heat is manifested in the form of disorder or the positive entropy change during the process. The thermodynamic parameters of micellization of CEDAB and CDMAB obtained by microcalorimetry in the presence of added NaBr with limits of their errors are presented in Table 3. The cmc’s of both of the surfactants appreciably decrease in the presence of low [NaBr]. The estimation of f following the conductance method in the (40) Moulik, S. P.; De, G. C.; Bhowmik, B. B.; Panda, A. K. J. Phys. Chem. B 1999, 103, 7122. (41) Moulik, S. P.; Digout, L. G.; Aylward, W. M.; Palepu, R. Langmuir 2000, 16, 3101. (42) Aylward, W. M.; Palepu, R.; Moulik, S. P. Can. J. Chem. 2001, 79, 1. (43) Digout, L.; Bern, K.; Palepu, R.; Moulik, S. P. J. Colloid Polym. Sci. 2001, 279, 655.
Micellization of CEDAB and CDMAB
Figure 7. Comparison of temperature-dependent entropy of micellization of CEDAB and CDMAB evaluated in different ways. CEDAB: (a) direct microcalorimetry; (b) microcalorimetric cmc’s processed at different temperatures by the van’t Hoff method with f; (c) conductometric cmc’s processed at different temperatures by the van’t Hoff method with f. CDMAB: (d) direct microcalorimetry; (e) microcalorimetric cmc’s processed at different temperatures by the van’t Hoff method with f; (f) conductometric cmc’s processed at different temperatures by the van’t Hoff method with f.
presence of salt becomes insensitive. But it has been observed that in the concentration range of 0-30 mmol dm-3 NaBr, the estimation of f by the conductance method is possible, and f has not varied appreciably from the value obtained without NaBr. Therefore, in the thermodynamic calculation, the f values of CEDAB and CDMAB at 303 K have been used. The effects of NaBr on the thermodynamics of micellization of CEDAB and CDMAB are on the whole comparable. The ∆H0m has shown a minimum at 5 mM [NaBr] for both of the surfactants. A General Comprehension. The cmc’s of CEDAB and CDMAB are fairly close, and they have appreciable temperature dependence. The cmc’s by calorimetry have shown a very mild trend of a minimum toward the lower end of the studied temperature. The conductometric results have not shown such a trend. The dependence of f on temperature has a concave pattern for CEDAB, and it is convex for CDMAB although the limits of variation of f in the studied temperature range are of comparable magnitudes. The ∆H0m results obtained from the van’t Hoff treatment and the direct microcalorimetry have shown differences. The method of calorimetry measures the integral enthalpy, whereas the van’t Hoff procedure deals with the differential enthalpy.14,38,39 The inequality between the two is, therefore, not unexpected.14,17,37-39 The quantification of the observed difference, however, remains to be understood. Along with association of surfactant monomer (micelle formation), there can arise interaction of solute components with the solvent (water) and nonspecific interactions in the system. The enthalpy change measured in a calorimeter thus corresponds to the sum total of all the involved heats, and hence it is called the integral heat of the process. The enthalpy change obtained from the van’t Hoff rationale refers only to the concerned equilibrium process (n(S+ or S- or S) h (S+ n or + + Sn or Sn), where S or S or S ) surfactant monomer, Sn or Sn or Sn ) micelle, and n ) aggregation number), and
Langmuir, Vol. 18, No. 8, 2002 3003
this is termed as the differential enthalpy change. Franks38 has thoroughly discussed the reasons for the discrepancy between the van’t Hoff and calorimetric enthalpy changes and has made a statement that “calorimetry yields integral heat, the van’t Hoff method gives rise to differential heat”. He has also stated that for agreement with calorimetry, there should not be any cooperative effect involved in the expression of ln K in the van’t Hoff model. The process of micellization often shows cooperativity. We have very recently made a thorough discussion on it based on calorimetric measurements on nonionic and ionic surfactants.11,14 A detailed discussion on this issue with reference to biochemical reaction equilibrium has been also made by Naghibi et al.39 The change in the aggregation number and f as well as the shape of the micelles with temperature may have contributions on the energetics of the process. The first has remained virtually invariant with temperature, and the second has been used in the calculation. We consider minor changes in the shape of the CEDAB and CDMAB micelles with temperature. The ∆H0m of CEDAB obtained by the van’t Hoff rationale has a wide range of variation, whereas the ∆H0m of CDMAB varies in a narrow range. The introduction of one more ethanolyl group for a methyl group in the head of CDMAB has made its self-aggregation process much less exothermic. The ∆S0m values for CEDAB likewise vary in a higher range compared to that for CDMAB, and the values even become negative at temperatures of g318 K in the case of the former. This is the manifestation of other (nonspecific) exothermic events during the micellization of CDMAB sensed by the microcalorimeter. How the replacement of one methyl group in CEDAB by an ethanolyl group as in CDMAB can make the above differences remains to be understood. The range of the ∆H0m values for both of the surfactant systems are on the whole comparable. But the ∆H0m values derived by the van’t Hoff method from the calorimetric results using eq 3 (in reality eq 10) in the first case (CEDAB) have a much wider range of variation compared to the second (CDMAB). The ∆S0m values obtained by combining the ∆G0m (obtained from eq 2) with these ∆H0m values using eq 4 likewise have poor agreement between the two surfactants, whereas those calculated using the microcalorimetric ∆H0m and the said ∆G0m values have fair agreement. The same discrepancy also prevails with ∆Cp0m. The ∆Cp0m values obtained for CEDAB by the van’t Hoff treatment are more negative than that for CDMAB. Moreover, they are higher than the calorimetric values for the first and lower for the second. In Table 4, the differences of ∆H0m, ∆S0m, and ∆Cp0m between CDMAB and CEDAB at different temperatures realized from microcalorimetric measurements are presented. These results show the effect of substitution of an ethanolyl group for a methyl group in the molecule and are designated as δ(∆H0m)sub, δ(∆S0m)sub, and δ(∆Cp0m)sub. The δ(∆H0m)sub decreases with temperature and becomes negative at temperatures of g298 K. The δ(∆S0m)sub has a similar trend, but it levels off at g313 K. The magnitude of (∆H0m)CDMAB exceeds that of (∆H0m)CEDAB at temperatures of g298 K with a concomitant decline in the corresponding (∆S0m)CDMAB compared to (∆S0m)CEDAB. The magnitude of (∆Cp0m)CDMAB is consequently higher than that of (∆Cp0m)CEDAB. The increasing δ(∆Cp0m)sub values with increasing temperature, therefore, are measures of
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Chatterjee et al.
Table 3. Salt (NaBr) Effect on the Critical Micellar Concentration and Thermodynamic Parametersa for the Micellization of CEDAB and CDMAB at 303 K CEDAB [NaBr]/mM
cmc/mM
-∆G0m/ kJ mol-1
0 2.5 5 10 20 25
0.91 ( 0.027 0.62 ( 0.019 0.45 ( 0.014 0.26 ( 0.008 0.19 ( 0.006 0.15 ( 0.005
47.3 49.0 50.4 52.7 54.0 55.0
a
CDMAB -∆H0m/ kJ mol-1
∆S0m/ J K-1 mol-1
[NaBr]/mM
cmc/mM
-∆G0m/ kJ mol-1
-∆H0m/ kJ mol-1
∆S0m/ J K-1 mol-1
15.35 12.04 11.75 12.80 13.20 13.31
105 122 127 132 135 137
0 5 10 20 25 30
0.83 ( 0.025 0.58 ( 0.017 0.34 ( 0.010 0.30 ( 0.009 0.27 ( 0.008 0.26 ( 0.008
46.9 48.4 50.7 51.2 51.7 51.8
16.82 12.22 11.46 12.53 13.01 11.97
99 119 130 128 128 132
The error limits are ∆G0m ) (3%, ∆H0m ) (3%, and ∆S0m ) (5% for both CEDAB and CDMAB.
Table 4. Effect of Replacement of a Methyl Group in CEDAB by an Ethanolyl Group Forming CDMAB on the Thermodynamic Parameters at Different Temperatures T/K
δ(∆H0m)sub/ kJ mol-1
δ(∆S0m)sub/ J K-1 mol-1
δ(∆Cp0m)sub/ J K-1 mol-1
288 293 298 303 308 313 318 323
0.50 1.0 -1.3 -1.5 -1.0 -1.3 -1.7 -2.2
2 3 -5 -6 -3 -5 -5 -5
-134 -118 -100 -83 -65 -49 -31 -13
Table 5. Microcalorimetrically Determined Thermodynamic Parametersa for the Micellizationb of CTAB at Three Different Temperaturesc T/K
cmc/mM
293 1.54 ( 0.077 298 1.05 ( 0.053 303 1.29 ( 0.039
∆H0m/ ∆S0m/ ∆Cp0m/ ∆G0m/ kJ mol-1 kJ mol-1 J K-1 mol-1 J K-1 mol-1 -48.6 -51.2 -51.1
-8.14 -10.14 -12.58
138.0 137.8 127.0
-444
The error limits are ∆G0m ) (3%, ∆H0m ) (3%, ∆S0m ) (5%, and ∆Cp0m ) (8%. b fCTAB ) 0.90 ( 0.027 is taken in the calculation. c Ionic surfactants usually show a decrease in cmc in the lower range of temperature; it is 298 K for CTAB. a
increasing softness of the micellar system per mole of substitution of an ethanolyl group for a methyl group. In this connection, it would be worthwhile to compare the calorimetrically derived thermodynamic results of micellization of CTAB with their error limits (Table 5) in relation to CEDAB (Table 1) and CDMAB (Table 2) at three temperatures, 293, 298, and 303 K. In this range of temperature, f of CTAB varies between 0.9 and 0.96, which is virtually invariant.5,7,9 We have assumed f ) 0.90 for the calculation of ∆G0m and hence ∆S0m. The -∆G0m values of CTAB are higher than those of CEDAB and CDMAB.
The -∆H0m values follow the order CTAB < CEDAB < CDMAB. The replacement of a -CH3 group by a -CH2CH2OH group makes the micellization process less spontaneous and more exothermic. The ∆S0m becomes more positive. The -∆Cp0m likewise follows the order of -∆H0m. All of the thermodynamic parameters have agreement regarding the substitution effect on the trimethylammonium headgroup of CTAB. Conclusions Although the cmc’s of CEDAB and CDMAB are close, their temperature dependence follows unequal trends. Although the ∆H0m values of the two surfactants obtained from calorimetry are of comparable magnitudes, the values obtained following the van’t Hoff rationale significantly differ. The ∆S0m values obtained by the van’t Hoff method also appreciably differ. Similar is the observation for ∆Cp0m. The extent of counterion binding by the two surfactants falls in the range of 65-74% in the studied temperature range of 288-323 K. Their aggregation numbers have been determined to be 123 and 112 for CEDAB and 105 and 113 for CDMAB at 293 and 323 K, respectively. The substitution of a methyl group on the surfactant head by an ethanolyl group has reduced the cmc and has made the process less spontaneous and more exothermic and organized. The salt NaBr has shown more cmc decreasing effect for CEDAB than CDMAB as well as more spontaneity of self-association and exothermic heat release of the former producing marginally greater disorder of the system. Acknowledgment. We thank the ICI R & T Centre, India, for financial support to the Centre for Surface Science, Jadavpur University, in the form of a project to perform the work. Thanks are also due to Ms. T. Dey, IACS, Calcutta, for fluorimetric measurements. LA010404K
